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Parker model of the solar wind Parker(1958) was the first to propose a model of the solar wind assuming a steady flow of plasma independent of time, as opposed to a static corona. He began from the mass and momentum conservation equations, taking time derivatives as zero since considering a steady flow… Assuming isothermal and B=0 he found a solution of the form…

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Weber and Davis (1967) derived a model which included the magnetic field – this leads to additional critical points in the equations

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The Heliosphere The heliosphere is the volume of space, enclosed within the interstellar medium, formed by, and which contains, the outflowing solar wind and the Sun's magnetic field. The size of the heliosphere (greater than 100 AU) is determined by a balance between the dynamic pressure of the solar wind and the pressure of the interstellar medium.

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Outer boundaries of the heliosphere The boundary between the solar wind plasma and interstellar plasma is known as the ‘heliopause’. Because the solar wind flow is supersonic it cannot ‘sense’ that it is approaching the heliopause. Thus a standing shock wave, the ‘termination shock’, must form at some distance inside the heliopause so that the flow is slowed to subsonic speeds. The solar wind plasma can then be deflected in the region between the termination shock and the heliopause to flow down the ‘heliotail’. Due to the motion of the heliosphere through the interstellar medium, the interstellar plasma is deflected to flow round the outside of the heliopause. Depending on the speed of this motion, a bow shock may form in the interstellar medium upstream of the heliopause.

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V1 crossed on 16 December 2004 at 94.5 AU V2 crossed in August 2007 at 84 AU Shock most visible in magnetic field magnitude increase However, many unexpected effects, especially in the particles

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V1 entered a new region of space on 25 August 2012 at AU Strong fluxes of galactic cosmic rays suggest good connection to the interstellar medium

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But magnetic field measurements had suggested spacecraft was still in fields connecting back to the southern hemisphere of the heliosphere…

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Heliospheric Spacecraft The first observations of the solar wind were made in the vicinity of the Earth in the early 1960s. Pioneer 10 and 11, launched in 1972 and 1973 were the first spacecraft to explore beyond 1 AU. Contact with these spacecraft have now been lost although Pioneer 10 was tracked to nearly 80 AU. Voyager 1 and 2 were launched in Both have scientific instruments still operating. Voyager 1 crossed the termination shock in 2004 at 94.5 AU, has now reached 126 AU and continues out towards the heliopause. Voyager 2, following behind at 103 AU, crossed the termination shock at 84 AU in Helios 1 and 2, launched in 1974 and 1976, explored the inner heliosphere in the ecliptic plane between 0.3 and 1 AU from the Sun. Ulysses, launched in 1990 into a ~6 year period orbit of the Sun inclined at 80.2° to the solar equator, with perihelion at 1.3 AU and aphelion at 5.4 AU. It was thus the first spacecraft to explore the 3D structure of the heliosphere over a large latitude range. Operations ceased in 2009 after nearly 3 orbits. STEREO, launched in 2006, consists of two spacecraft at 1 AU separating in solar longitude ahead of and behind the Earth. They carry instrumentation aimed at obtaining stereoscopic views of the Sun and to make multi-point in- situ measurements of the solar wind.

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The heliospheric magnetic field The heliospheric magnetic field is a result of the Sun’s magnetic field being carried outward, frozen in to the solar wind. Within the corona, the magnetic field forces dominate the plasma forces. As the field strength decreases with distance, beyond the Alfvén radius at a few solar radii, the plasma flow becomes dominant, and the field lines are constrained to move with the solar wind. Model of Pneumann and Kopp (1971)

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Model of Banaskiewicz et al (1998)

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For modelling purposes, a ‘source surface’ is assumed, typically ~2.5 solar radii, at which the magnetic field lines are constrained to be radial. (http://wso.stanford.edu/)

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Examples of potential field models of the corona… Bravo et al (1998)

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The heliospheric current sheet forms where outward field lines from one hemisphere meet inward field lines from the other hemisphere.

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Near solar minimum when the Sun’s dipole field is dominant, the current sheet can be viewed as a plane tilted at the same angle as the dipole, embedded in the band of slow solar wind. Therefore interplanetary spacecraft observe current sheet crossings up to a latitude equal to the dipole tilt angle. Smith (1997)

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Ulysses passages above the maximum latitude of the current sheet…

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The current sheet mapped out into the heliosphere… Jokipii and Thomas (1981)

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The Parker Spiral Field The solar magnetic field is frozen in to the radial outflowing solar wind. Thus, due to the Sun’s rotation, the magnetic field lines adopt an Archimedean spiral configuration. The angle to the radial direction of the magnetic field depends on distance, latitude and the local solar wind velocity. Parker (1963)

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Measurements near the ecliptic plane are found to fit this picture to a good approximation. Forsyth et al (1996)

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Moving away from the equator, field lines gradually become less tightly wound with latitude until a field line originating exactly from the pole remains purely radial. Ulysses showed that this was followed to a good first approximation also at high latitudes.

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In an attempt to explain Ulysses energetic particle fluxes at high latitudes a more complex field model was proposed by Fisk and co-workers. Fisk and Jokipii (1999) Fisk (1996)

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Others argue that the particles reach high latitudes as a result of field line mixing due to the random motion of footpoints in the corona… Jokipii and Kota (1989)Giacalone (1999)

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Dependence of Field Strength on Latitude Assuming that the magnetic field is radial at the ‘source surface’, the radial component of the magnetic field can be used to infer the field strength near the Sun since r 2 B r is a constant. Ulysses observations showed that r 2 B r had no dependence on latitude. This implies that the latitudinal magnetic pressure gradient associated with strong photospheric polar fields must have relaxed by the outer corona. Smith and Balogh (1995)

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South North Smoothed average Wilcox Solar Obsevatory (http://wso.stanford.edu) Photospheric field also reduced…

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At the recent solar minimum the heliospheric magnetic field at 1 AU was at the lowest since spacecraft records began… Owens et al (2008)

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…and the solar wind was at its weakest in the space age McComas et al (2008)

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Fast and Slow Solar Wind Since the first spacecraft observations it was known that the solar wind was divided into streams of slow (~400 km/s) and fast (>500 km/s) wind. Hundhausen (1995)

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Ulysses found continuous fast solar wind (~750 km/s) at high latitudes at solar minimum in agreement with the idea that fast solar wind originated in coronal holes. This fast wind was associated with large stable polar coronal holes. Slow solar wind is associated with the streamers seen in coronagraph images, but its exact source is unclear. McComas et al (1998)

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Close to solar minimum the flow pattern close to the Sun can be approximated as a band of slow wind at low latitudes, centred on the Sun’s dipole equator, with fast wind at all higher latitudes. This pattern of fast and slow solar wind is occasionally disturbed by transient flows associated with coronal mass ejections. Pizzo (1991)

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Solar cycle evolution The tilt of the underlying solar dipole field and hence of the heliospheric current sheet and the band of slow wind is a function of the solar cycle, with least tilt near solar minimum. Alternatively, the evolution of the coronal field can be viewed as the strength of the dipole component decreasing as solar activity increases so that the higher order components of the solar field have a greater effect. Suess et al (1998)

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This evolution culminates in the reversal of the Sun’s magnetic field during the solar maximum period.

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At solar maximum the large polar coronal holes disappear and are replaced by smaller, generally short lived coronal holes at all latitudes. Ulysses observed fast and slow wind at all latitudes in the southern hemisphere. McComas et al, (2008)

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Corotating Interaction Regions Interaction regions form wherever fast solar wind ‘catches up’ with slower wind ahead of it. A compression region forms where the magnetic field lines and plasma ‘pile up’. The resulting pressure waves can steepen into shocks. When a fast solar wind stream originates from a stable coronal hole persisting over many solar rotations, the resulting interaction region pattern corotates with the Sun. Ulysses provided new results on the three dimensional geometry of Corotating Interaction regions. Pizzo (1985)

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Interaction Regions in 1D Because of the Sun’s rotation faster plasma emitted along a particular radial line, catches up with slower plasma emitted in the same direction at an earlier time. The plasma streams cannot interpenetrate because of the frozen in magnetic field. A compression region builds up leading the fast stream, while a rarefaction develops behind. Due to pressure gradients the compression region expands at the fast mode speed. A forward wave develops on the leading edge and a reverse wave on the trailing edge. Gosling (1998)

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If the speed difference between the streams is greater than ~2 times the fast mode speed then the stream front steepens faster than the high pressure region can expand. The pressure waves then develop into shocks. These propagate faster than the fast mode speed allowing the compression region to expand again. The forward wave/shock accelerates slow plasma ahead of the interaction region. The reverse wave/shock decelerates fast plasma trailing the interaction region. It propagates towards the Sun in the solar wind frame but is convected outwards across a stationary observer. Hundhausen (1973)

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Ulysses observed two clear intervals of CIRs during its first orbit Forsyth and Gosling (2001)

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Interaction Regions in 2D and 3D In 2D the interaction region forms an Archimedean spiral oriented between the tighter spirals of the slow wind and the less tight spirals of the fast wind If the sources are quasi-stationary compared to the solar rotation period, then the entire pattern corotates with the Sun. Because of the spiral geometry, forward waves/shocks have a westward component of propagation. Reverse waves/ shocks have an eastward component of propagation. Pizzo (1985)

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This behaviour was shown to be consistent with the source region of slow speed solar wind forming a low latitude band symmetrical about the Sun’s magnetic equator, i.e. tilted with respect the rotation axis. Pizzo (1991) Gosling (1996)

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Some open questions The coronal heating problem is not yet solved. The outer boundaries of the heliosphere: New understanding is coming from the Voyager termination shock and heliopause crossings. The high latitude solar and coronal magnetic fields – a major source of uncertainty in models. (Solar Orbiter) What is the origin of the recent extended and deep solar minimum? Is there a persistent north-south asymmetry in the corona and heliosphere? Coronal Mass Ejections: e.g. initiation, acceleration, large scale structure, solar origin of the properties measured in interplanetary space, evolution during propagation. Do coronal mass ejections play a role in the solar cycle reversal of the heliospheric magnetic field?